I've been thinking about this for a while and still cannot come up with a way to show that all finite languages are regular. I know that all finite languages consist of finite number of strings that are themselves finite and hence there should be either a DFA that recognizes them or a regular expression that can be constructed for each string but I am not sure if this will suffice as proof.
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Yes, it suffices. – Brian M. Scott May 08 '15 at 19:47
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Show that a language consisting of a single word is regular, and show that the union of two regular languages is regular. – Qiaochu Yuan May 08 '15 at 19:56
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Thanks for the conformation, yes using union is a good idea too. – Vector_13 May 08 '15 at 20:01
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Possible duplicate of Formally prove that every finite language is regular – Kumar Sep 23 '19 at 19:46